# Properties

 Label 76.6.e.a.49.1 Level $76$ Weight $6$ Character 76.49 Analytic conductor $12.189$ Analytic rank $0$ Dimension $18$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$76 = 2^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 76.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$12.1891703058$$ Analytic rank: $$0$$ Dimension: $$18$$ Relative dimension: $$9$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ Defining polynomial: $$x^{18} - 2 x^{17} + 1540 x^{16} - 768 x^{15} + 1608492 x^{14} - 1027368 x^{13} + 897054160 x^{12} - 1275481376 x^{11} + 361098181456 x^{10} - 863969476320 x^{9} + 79755165392064 x^{8} - 375077568148992 x^{7} + 12736924096193536 x^{6} - 57314532742553600 x^{5} + 977121800205220864 x^{4} - 4977732006498379776 x^{3} + 53672321824823513088 x^{2} - 185653809995679793152 x + 804303742853852430336$$ Coefficient ring: $$\Z[a_1, \ldots, a_{19}]$$ Coefficient ring index: $$2^{16}\cdot 3^{3}\cdot 5^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 49.1 Root $$14.2764 + 24.7275i$$ of defining polynomial Character $$\chi$$ $$=$$ 76.49 Dual form 76.6.e.a.45.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-14.7764 + 25.5935i) q^{3} +(35.6401 - 61.7304i) q^{5} +252.315 q^{7} +(-315.186 - 545.918i) q^{9} +O(q^{10})$$ $$q+(-14.7764 + 25.5935i) q^{3} +(35.6401 - 61.7304i) q^{5} +252.315 q^{7} +(-315.186 - 545.918i) q^{9} +88.0323 q^{11} +(307.862 + 533.232i) q^{13} +(1053.27 + 1824.31i) q^{15} +(285.543 - 494.575i) q^{17} +(361.524 + 1531.47i) q^{19} +(-3728.32 + 6457.64i) q^{21} +(-1214.28 - 2103.20i) q^{23} +(-977.931 - 1693.83i) q^{25} +11447.9 q^{27} +(1142.82 + 1979.43i) q^{29} +3684.20 q^{31} +(-1300.80 + 2253.06i) q^{33} +(8992.54 - 15575.5i) q^{35} +3064.28 q^{37} -18196.4 q^{39} +(-1246.89 + 2159.67i) q^{41} +(-2450.11 + 4243.71i) q^{43} -44933.0 q^{45} +(8786.51 + 15218.7i) q^{47} +46856.0 q^{49} +(8438.61 + 14616.1i) q^{51} +(-12713.9 - 22021.1i) q^{53} +(3137.48 - 5434.27i) q^{55} +(-44537.7 - 13377.0i) q^{57} +(-11756.9 + 20363.5i) q^{59} +(9886.00 + 17123.1i) q^{61} +(-79526.2 - 137743. i) q^{63} +43888.8 q^{65} +(-13694.3 - 23719.2i) q^{67} +71771.0 q^{69} +(-16750.0 + 29011.9i) q^{71} +(-8986.08 + 15564.3i) q^{73} +57801.3 q^{75} +22211.9 q^{77} +(41242.9 - 71434.8i) q^{79} +(-92569.6 + 160335. i) q^{81} +40274.4 q^{83} +(-20353.5 - 35253.4i) q^{85} -67547.4 q^{87} +(-27641.5 - 47876.5i) q^{89} +(77678.2 + 134543. i) q^{91} +(-54439.3 + 94291.7i) q^{93} +(107423. + 32264.7i) q^{95} +(13348.8 - 23120.7i) q^{97} +(-27746.6 - 48058.4i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} + O(q^{10})$$ $$18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} - 320q^{11} + 227q^{13} - 101q^{15} + 179q^{17} - 868q^{19} - 5700q^{21} - 3425q^{23} - 7054q^{25} + 14722q^{27} - 7349q^{29} - 9960q^{31} - 2998q^{33} + 15888q^{35} + 26444q^{37} - 30246q^{39} - 7311q^{41} - 8283q^{43} - 62164q^{45} + 37603q^{47} + 124738q^{49} + 47227q^{51} - 20337q^{53} + 716q^{55} - 57555q^{57} - 74455q^{59} - 7569q^{61} - 52544q^{63} + 188998q^{65} - 26177q^{67} + 116282q^{69} - 53463q^{71} - 14103q^{73} + 120912q^{75} - 31960q^{77} + 31825q^{79} - 21137q^{81} + 82600q^{83} - 50787q^{85} - 339766q^{87} - 155197q^{89} - 2800q^{91} - 46460q^{93} + 49315q^{95} + 111241q^{97} - 193544q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$$.

 $$n$$ $$21$$ $$39$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −14.7764 + 25.5935i −0.947909 + 1.64183i −0.198088 + 0.980184i $$0.563473\pi$$
−0.749820 + 0.661642i $$0.769860\pi$$
$$4$$ 0 0
$$5$$ 35.6401 61.7304i 0.637549 1.10427i −0.348420 0.937339i $$-0.613282\pi$$
0.985969 0.166929i $$-0.0533850\pi$$
$$6$$ 0 0
$$7$$ 252.315 1.94625 0.973125 0.230279i $$-0.0739637\pi$$
0.973125 + 0.230279i $$0.0739637\pi$$
$$8$$ 0 0
$$9$$ −315.186 545.918i −1.29706 2.24658i
$$10$$ 0 0
$$11$$ 88.0323 0.219362 0.109681 0.993967i $$-0.465017\pi$$
0.109681 + 0.993967i $$0.465017\pi$$
$$12$$ 0 0
$$13$$ 307.862 + 533.232i 0.505239 + 0.875100i 0.999982 + 0.00606030i $$0.00192907\pi$$
−0.494742 + 0.869040i $$0.664738\pi$$
$$14$$ 0 0
$$15$$ 1053.27 + 1824.31i 1.20868 + 2.09349i
$$16$$ 0 0
$$17$$ 285.543 494.575i 0.239634 0.415059i −0.720975 0.692961i $$-0.756306\pi$$
0.960609 + 0.277902i $$0.0896391\pi$$
$$18$$ 0 0
$$19$$ 361.524 + 1531.47i 0.229748 + 0.973250i
$$20$$ 0 0
$$21$$ −3728.32 + 6457.64i −1.84487 + 3.19540i
$$22$$ 0 0
$$23$$ −1214.28 2103.20i −0.478630 0.829011i 0.521070 0.853514i $$-0.325533\pi$$
−0.999700 + 0.0245027i $$0.992200\pi$$
$$24$$ 0 0
$$25$$ −977.931 1693.83i −0.312938 0.542024i
$$26$$ 0 0
$$27$$ 11447.9 3.02216
$$28$$ 0 0
$$29$$ 1142.82 + 1979.43i 0.252339 + 0.437064i 0.964169 0.265288i $$-0.0854669\pi$$
−0.711830 + 0.702351i $$0.752134\pi$$
$$30$$ 0 0
$$31$$ 3684.20 0.688555 0.344278 0.938868i $$-0.388124\pi$$
0.344278 + 0.938868i $$0.388124\pi$$
$$32$$ 0 0
$$33$$ −1300.80 + 2253.06i −0.207935 + 0.360153i
$$34$$ 0 0
$$35$$ 8992.54 15575.5i 1.24083 2.14918i
$$36$$ 0 0
$$37$$ 3064.28 0.367980 0.183990 0.982928i $$-0.441099\pi$$
0.183990 + 0.982928i $$0.441099\pi$$
$$38$$ 0 0
$$39$$ −18196.4 −1.91568
$$40$$ 0 0
$$41$$ −1246.89 + 2159.67i −0.115842 + 0.200645i −0.918116 0.396311i $$-0.870290\pi$$
0.802274 + 0.596956i $$0.203623\pi$$
$$42$$ 0 0
$$43$$ −2450.11 + 4243.71i −0.202075 + 0.350005i −0.949197 0.314682i $$-0.898102\pi$$
0.747122 + 0.664687i $$0.231435\pi$$
$$44$$ 0 0
$$45$$ −44933.0 −3.30776
$$46$$ 0 0
$$47$$ 8786.51 + 15218.7i 0.580192 + 1.00492i 0.995456 + 0.0952210i $$0.0303558\pi$$
−0.415264 + 0.909701i $$0.636311\pi$$
$$48$$ 0 0
$$49$$ 46856.0 2.78789
$$50$$ 0 0
$$51$$ 8438.61 + 14616.1i 0.454303 + 0.786876i
$$52$$ 0 0
$$53$$ −12713.9 22021.1i −0.621712 1.07684i −0.989167 0.146795i $$-0.953104\pi$$
0.367455 0.930041i $$-0.380229\pi$$
$$54$$ 0 0
$$55$$ 3137.48 5434.27i 0.139854 0.242234i
$$56$$ 0 0
$$57$$ −44537.7 13377.0i −1.81569 0.545345i
$$58$$ 0 0
$$59$$ −11756.9 + 20363.5i −0.439706 + 0.761592i −0.997667 0.0682748i $$-0.978251\pi$$
0.557961 + 0.829867i $$0.311584\pi$$
$$60$$ 0 0
$$61$$ 9886.00 + 17123.1i 0.340170 + 0.589192i 0.984464 0.175586i $$-0.0561820\pi$$
−0.644294 + 0.764778i $$0.722849\pi$$
$$62$$ 0 0
$$63$$ −79526.2 137743.i −2.52440 4.37240i
$$64$$ 0 0
$$65$$ 43888.8 1.28846
$$66$$ 0 0
$$67$$ −13694.3 23719.2i −0.372694 0.645525i 0.617285 0.786740i $$-0.288233\pi$$
−0.989979 + 0.141214i $$0.954899\pi$$
$$68$$ 0 0
$$69$$ 71771.0 1.81479
$$70$$ 0 0
$$71$$ −16750.0 + 29011.9i −0.394339 + 0.683014i −0.993017 0.117975i $$-0.962360\pi$$
0.598678 + 0.800990i $$0.295693\pi$$
$$72$$ 0 0
$$73$$ −8986.08 + 15564.3i −0.197362 + 0.341841i −0.947672 0.319245i $$-0.896571\pi$$
0.750310 + 0.661086i $$0.229904\pi$$
$$74$$ 0 0
$$75$$ 57801.3 1.18655
$$76$$ 0 0
$$77$$ 22211.9 0.426932
$$78$$ 0 0
$$79$$ 41242.9 71434.8i 0.743501 1.28778i −0.207391 0.978258i $$-0.566497\pi$$
0.950892 0.309523i $$-0.100169\pi$$
$$80$$ 0 0
$$81$$ −92569.6 + 160335.i −1.56767 + 2.71529i
$$82$$ 0 0
$$83$$ 40274.4 0.641702 0.320851 0.947130i $$-0.396031\pi$$
0.320851 + 0.947130i $$0.396031\pi$$
$$84$$ 0 0
$$85$$ −20353.5 35253.4i −0.305557 0.529241i
$$86$$ 0 0
$$87$$ −67547.4 −0.956777
$$88$$ 0 0
$$89$$ −27641.5 47876.5i −0.369902 0.640689i 0.619648 0.784880i $$-0.287275\pi$$
−0.989550 + 0.144191i $$0.953942\pi$$
$$90$$ 0 0
$$91$$ 77678.2 + 134543.i 0.983322 + 1.70316i
$$92$$ 0 0
$$93$$ −54439.3 + 94291.7i −0.652688 + 1.13049i
$$94$$ 0 0
$$95$$ 107423. + 32264.7i 1.22120 + 0.366791i
$$96$$ 0 0
$$97$$ 13348.8 23120.7i 0.144049 0.249501i −0.784968 0.619536i $$-0.787321\pi$$
0.929018 + 0.370035i $$0.120654\pi$$
$$98$$ 0 0
$$99$$ −27746.6 48058.4i −0.284525 0.492812i
$$100$$ 0 0
$$101$$ −60668.2 105080.i −0.591777 1.02499i −0.993993 0.109443i $$-0.965093\pi$$
0.402216 0.915545i $$-0.368240\pi$$
$$102$$ 0 0
$$103$$ −123258. −1.14478 −0.572392 0.819980i $$-0.693985\pi$$
−0.572392 + 0.819980i $$0.693985\pi$$
$$104$$ 0 0
$$105$$ 265755. + 460302.i 2.35239 + 4.07445i
$$106$$ 0 0
$$107$$ 225615. 1.90506 0.952529 0.304449i $$-0.0984722\pi$$
0.952529 + 0.304449i $$0.0984722\pi$$
$$108$$ 0 0
$$109$$ −25583.8 + 44312.5i −0.206253 + 0.357240i −0.950531 0.310629i $$-0.899460\pi$$
0.744279 + 0.667869i $$0.232793\pi$$
$$110$$ 0 0
$$111$$ −45279.2 + 78425.8i −0.348812 + 0.604160i
$$112$$ 0 0
$$113$$ −113870. −0.838909 −0.419454 0.907776i $$-0.637779\pi$$
−0.419454 + 0.907776i $$0.637779\pi$$
$$114$$ 0 0
$$115$$ −173108. −1.22060
$$116$$ 0 0
$$117$$ 194067. 336134.i 1.31065 2.27012i
$$118$$ 0 0
$$119$$ 72046.9 124789.i 0.466388 0.807808i
$$120$$ 0 0
$$121$$ −153301. −0.951881
$$122$$ 0 0
$$123$$ −36849.1 63824.5i −0.219616 0.380386i
$$124$$ 0 0
$$125$$ 83336.4 0.477045
$$126$$ 0 0
$$127$$ −23234.7 40243.6i −0.127828 0.221405i 0.795007 0.606601i $$-0.207467\pi$$
−0.922835 + 0.385196i $$0.874134\pi$$
$$128$$ 0 0
$$129$$ −72407.6 125414.i −0.383098 0.663546i
$$130$$ 0 0
$$131$$ 142237. 246361.i 0.724157 1.25428i −0.235163 0.971956i $$-0.575562\pi$$
0.959320 0.282321i $$-0.0911044\pi$$
$$132$$ 0 0
$$133$$ 91217.9 + 386413.i 0.447148 + 1.89419i
$$134$$ 0 0
$$135$$ 408006. 706687.i 1.92678 3.33728i
$$136$$ 0 0
$$137$$ −143955. 249337.i −0.655277 1.13497i −0.981824 0.189792i $$-0.939219\pi$$
0.326547 0.945181i $$-0.394115\pi$$
$$138$$ 0 0
$$139$$ 88821.1 + 153843.i 0.389923 + 0.675367i 0.992439 0.122740i $$-0.0391681\pi$$
−0.602515 + 0.798107i $$0.705835\pi$$
$$140$$ 0 0
$$141$$ −519333. −2.19988
$$142$$ 0 0
$$143$$ 27101.8 + 46941.6i 0.110830 + 0.191963i
$$144$$ 0 0
$$145$$ 162921. 0.643514
$$146$$ 0 0
$$147$$ −692365. + 1.19921e6i −2.64266 + 4.57723i
$$148$$ 0 0
$$149$$ −81129.1 + 140520.i −0.299372 + 0.518527i −0.975992 0.217805i $$-0.930110\pi$$
0.676621 + 0.736332i $$0.263444\pi$$
$$150$$ 0 0
$$151$$ −449650. −1.60484 −0.802420 0.596760i $$-0.796455\pi$$
−0.802420 + 0.596760i $$0.796455\pi$$
$$152$$ 0 0
$$153$$ −359996. −1.24328
$$154$$ 0 0
$$155$$ 131305. 227427.i 0.438988 0.760349i
$$156$$ 0 0
$$157$$ −27389.5 + 47440.1i −0.0886820 + 0.153602i −0.906954 0.421229i $$-0.861599\pi$$
0.818272 + 0.574831i $$0.194932\pi$$
$$158$$ 0 0
$$159$$ 751464. 2.35730
$$160$$ 0 0
$$161$$ −306382. 530669.i −0.931533 1.61346i
$$162$$ 0 0
$$163$$ 207755. 0.612467 0.306233 0.951956i $$-0.400931\pi$$
0.306233 + 0.951956i $$0.400931\pi$$
$$164$$ 0 0
$$165$$ 92721.5 + 160598.i 0.265137 + 0.459231i
$$166$$ 0 0
$$167$$ −136696. 236765.i −0.379284 0.656940i 0.611674 0.791110i $$-0.290496\pi$$
−0.990958 + 0.134170i $$0.957163\pi$$
$$168$$ 0 0
$$169$$ −3910.94 + 6773.94i −0.0105333 + 0.0182442i
$$170$$ 0 0
$$171$$ 722110. 680060.i 1.88848 1.77851i
$$172$$ 0 0
$$173$$ −262508. + 454677.i −0.666848 + 1.15501i 0.311933 + 0.950104i $$0.399024\pi$$
−0.978781 + 0.204910i $$0.934310\pi$$
$$174$$ 0 0
$$175$$ −246747. 427378.i −0.609055 1.05491i
$$176$$ 0 0
$$177$$ −347449. 601800.i −0.833601 1.44384i
$$178$$ 0 0
$$179$$ −13590.9 −0.0317041 −0.0158520 0.999874i $$-0.505046\pi$$
−0.0158520 + 0.999874i $$0.505046\pi$$
$$180$$ 0 0
$$181$$ −36970.5 64034.9i −0.0838802 0.145285i 0.821033 0.570880i $$-0.193398\pi$$
−0.904913 + 0.425596i $$0.860065\pi$$
$$182$$ 0 0
$$183$$ −584319. −1.28980
$$184$$ 0 0
$$185$$ 109211. 189160.i 0.234606 0.406349i
$$186$$ 0 0
$$187$$ 25137.0 43538.6i 0.0525666 0.0910480i
$$188$$ 0 0
$$189$$ 2.88849e6 5.88189
$$190$$ 0 0
$$191$$ −522570. −1.03648 −0.518240 0.855235i $$-0.673413\pi$$
−0.518240 + 0.855235i $$0.673413\pi$$
$$192$$ 0 0
$$193$$ 12411.0 21496.6i 0.0239836 0.0415409i −0.853784 0.520627i $$-0.825698\pi$$
0.877768 + 0.479086i $$0.159032\pi$$
$$194$$ 0 0
$$195$$ −648520. + 1.12327e6i −1.22134 + 2.11543i
$$196$$ 0 0
$$197$$ −363318. −0.666993 −0.333496 0.942751i $$-0.608228\pi$$
−0.333496 + 0.942751i $$0.608228\pi$$
$$198$$ 0 0
$$199$$ 40673.4 + 70448.5i 0.0728078 + 0.126107i 0.900131 0.435620i $$-0.143471\pi$$
−0.827323 + 0.561726i $$0.810137\pi$$
$$200$$ 0 0
$$201$$ 809411. 1.41312
$$202$$ 0 0
$$203$$ 288352. + 499440.i 0.491114 + 0.850635i
$$204$$ 0 0
$$205$$ 88878.3 + 153942.i 0.147710 + 0.255842i
$$206$$ 0 0
$$207$$ −765449. + 1.32580e6i −1.24162 + 2.15056i
$$208$$ 0 0
$$209$$ 31825.8 + 134819.i 0.0503980 + 0.213494i
$$210$$ 0 0
$$211$$ −235569. + 408017.i −0.364260 + 0.630917i −0.988657 0.150190i $$-0.952011\pi$$
0.624397 + 0.781107i $$0.285345\pi$$
$$212$$ 0 0
$$213$$ −495011. 857384.i −0.747594 1.29487i
$$214$$ 0 0
$$215$$ 174644. + 302492.i 0.257666 + 0.446291i
$$216$$ 0 0
$$217$$ 929580. 1.34010
$$218$$ 0 0
$$219$$ −265564. 459971.i −0.374162 0.648068i
$$220$$ 0 0
$$221$$ 351631. 0.484291
$$222$$ 0 0
$$223$$ −650115. + 1.12603e6i −0.875443 + 1.51631i −0.0191530 + 0.999817i $$0.506097\pi$$
−0.856290 + 0.516495i $$0.827236\pi$$
$$224$$ 0 0
$$225$$ −616460. + 1.06774e6i −0.811799 + 1.40608i
$$226$$ 0 0
$$227$$ −73342.4 −0.0944692 −0.0472346 0.998884i $$-0.515041\pi$$
−0.0472346 + 0.998884i $$0.515041\pi$$
$$228$$ 0 0
$$229$$ −1.25234e6 −1.57809 −0.789046 0.614335i $$-0.789424\pi$$
−0.789046 + 0.614335i $$0.789424\pi$$
$$230$$ 0 0
$$231$$ −328213. + 568481.i −0.404693 + 0.700949i
$$232$$ 0 0
$$233$$ 544644. 943351.i 0.657238 1.13837i −0.324089 0.946027i $$-0.605058\pi$$
0.981328 0.192344i $$-0.0616089\pi$$
$$234$$ 0 0
$$235$$ 1.25261e6 1.47960
$$236$$ 0 0
$$237$$ 1.21885e6 + 2.11110e6i 1.40954 + 2.44140i
$$238$$ 0 0
$$239$$ 928359. 1.05129 0.525644 0.850705i $$-0.323825\pi$$
0.525644 + 0.850705i $$0.323825\pi$$
$$240$$ 0 0
$$241$$ −49744.9 86160.6i −0.0551703 0.0955578i 0.837121 0.547017i $$-0.184237\pi$$
−0.892292 + 0.451460i $$0.850904\pi$$
$$242$$ 0 0
$$243$$ −1.34477e6 2.32921e6i −1.46094 2.53043i
$$244$$ 0 0
$$245$$ 1.66995e6 2.89244e6i 1.77742 3.07857i
$$246$$ 0 0
$$247$$ −705329. + 664256.i −0.735613 + 0.692777i
$$248$$ 0 0
$$249$$ −595112. + 1.03076e6i −0.608275 + 1.05356i
$$250$$ 0 0
$$251$$ −190030. 329141.i −0.190387 0.329760i 0.754992 0.655735i $$-0.227641\pi$$
−0.945379 + 0.325975i $$0.894308\pi$$
$$252$$ 0 0
$$253$$ −106896. 185149.i −0.104993 0.181853i
$$254$$ 0 0
$$255$$ 1.20301e6 1.15856
$$256$$ 0 0
$$257$$ −552645. 957209.i −0.521931 0.904012i −0.999675 0.0255121i $$-0.991878\pi$$
0.477743 0.878500i $$-0.341455\pi$$
$$258$$ 0 0
$$259$$ 773166. 0.716182
$$260$$ 0 0
$$261$$ 720404. 1.24778e6i 0.654598 1.13380i
$$262$$ 0 0
$$263$$ −276003. + 478051.i −0.246050 + 0.426172i −0.962426 0.271543i $$-0.912466\pi$$
0.716376 + 0.697714i $$0.245800\pi$$
$$264$$ 0 0
$$265$$ −1.81250e6 −1.58549
$$266$$ 0 0
$$267$$ 1.63377e6 1.40253
$$268$$ 0 0
$$269$$ 859906. 1.48940e6i 0.724553 1.25496i −0.234604 0.972091i $$-0.575379\pi$$
0.959158 0.282872i $$-0.0912872\pi$$
$$270$$ 0 0
$$271$$ 451795. 782532.i 0.373696 0.647260i −0.616435 0.787406i $$-0.711424\pi$$
0.990131 + 0.140146i $$0.0447571\pi$$
$$272$$ 0 0
$$273$$ −4.59123e6 −3.72840
$$274$$ 0 0
$$275$$ −86089.5 149111.i −0.0686465 0.118899i
$$276$$ 0 0
$$277$$ −1.04518e6 −0.818447 −0.409223 0.912434i $$-0.634200\pi$$
−0.409223 + 0.912434i $$0.634200\pi$$
$$278$$ 0 0
$$279$$ −1.16121e6 2.01127e6i −0.893099 1.54689i
$$280$$ 0 0
$$281$$ −213159. 369202.i −0.161041 0.278932i 0.774201 0.632940i $$-0.218152\pi$$
−0.935242 + 0.354008i $$0.884819\pi$$
$$282$$ 0 0
$$283$$ −29882.7 + 51758.4i −0.0221796 + 0.0384162i −0.876902 0.480669i $$-0.840394\pi$$
0.854723 + 0.519085i $$0.173727\pi$$
$$284$$ 0 0
$$285$$ −2.41310e6 + 2.27258e6i −1.75980 + 1.65732i
$$286$$ 0 0
$$287$$ −314609. + 544918.i −0.225458 + 0.390505i
$$288$$ 0 0
$$289$$ 546859. + 947188.i 0.385151 + 0.667101i
$$290$$ 0 0
$$291$$ 394494. + 683284.i 0.273092 + 0.473008i
$$292$$ 0 0
$$293$$ 1.17326e6 0.798410 0.399205 0.916862i $$-0.369286\pi$$
0.399205 + 0.916862i $$0.369286\pi$$
$$294$$ 0 0
$$295$$ 838032. + 1.45151e6i 0.560668 + 0.971105i
$$296$$ 0 0
$$297$$ 1.00779e6 0.662947
$$298$$ 0 0
$$299$$ 747661. 1.29499e6i 0.483645 0.837698i
$$300$$ 0 0
$$301$$ −618199. + 1.07075e6i −0.393289 + 0.681197i
$$302$$ 0 0
$$303$$ 3.58584e6 2.24380
$$304$$ 0 0
$$305$$ 1.40935e6 0.867501
$$306$$ 0 0
$$307$$ −252040. + 436545.i −0.152624 + 0.264353i −0.932191 0.361966i $$-0.882106\pi$$
0.779567 + 0.626318i $$0.215439\pi$$
$$308$$ 0 0
$$309$$ 1.82132e6 3.15462e6i 1.08515 1.87954i
$$310$$ 0 0
$$311$$ 2.39525e6 1.40426 0.702132 0.712046i $$-0.252231\pi$$
0.702132 + 0.712046i $$0.252231\pi$$
$$312$$ 0 0
$$313$$ −1.06455e6 1.84385e6i −0.614193 1.06381i −0.990525 0.137329i $$-0.956148\pi$$
0.376332 0.926485i $$-0.377185\pi$$
$$314$$ 0 0
$$315$$ −1.13373e7 −6.43773
$$316$$ 0 0
$$317$$ −399285. 691581.i −0.223169 0.386541i 0.732599 0.680660i $$-0.238307\pi$$
−0.955769 + 0.294120i $$0.904974\pi$$
$$318$$ 0 0
$$319$$ 100605. + 174254.i 0.0553535 + 0.0958750i
$$320$$ 0 0
$$321$$ −3.33378e6 + 5.77428e6i −1.80582 + 3.12777i
$$322$$ 0 0
$$323$$ 860657. + 258500.i 0.459012 + 0.137865i
$$324$$ 0 0
$$325$$ 602135. 1.04293e6i 0.316217 0.547704i
$$326$$ 0 0
$$327$$ −756075. 1.30956e6i −0.391017 0.677261i
$$328$$ 0 0
$$329$$ 2.21697e6 + 3.83991e6i 1.12920 + 1.95583i
$$330$$ 0 0
$$331$$ −224790. −0.112773 −0.0563867 0.998409i $$-0.517958\pi$$
−0.0563867 + 0.998409i $$0.517958\pi$$
$$332$$ 0 0
$$333$$ −965819. 1.67285e6i −0.477293 0.826696i
$$334$$ 0 0
$$335$$ −1.95226e6 −0.950444
$$336$$ 0 0
$$337$$ 1.02795e6 1.78046e6i 0.493056 0.853998i −0.506912 0.861998i $$-0.669213\pi$$
0.999968 + 0.00799964i $$0.00254639\pi$$
$$338$$ 0 0
$$339$$ 1.68260e6 2.91435e6i 0.795209 1.37734i
$$340$$ 0 0
$$341$$ 324329. 0.151043
$$342$$ 0 0
$$343$$ 7.58183e6 3.47967
$$344$$ 0 0
$$345$$ 2.55792e6 4.43046e6i 1.15702 2.00401i
$$346$$ 0 0
$$347$$ −1.48248e6 + 2.56773e6i −0.660946 + 1.14479i 0.319422 + 0.947613i $$0.396511\pi$$
−0.980368 + 0.197179i $$0.936822\pi$$
$$348$$ 0 0
$$349$$ 2.25013e6 0.988883 0.494441 0.869211i $$-0.335373\pi$$
0.494441 + 0.869211i $$0.335373\pi$$
$$350$$ 0 0
$$351$$ 3.52438e6 + 6.10441e6i 1.52692 + 2.64470i
$$352$$ 0 0
$$353$$ −1.72711e6 −0.737706 −0.368853 0.929488i $$-0.620249\pi$$
−0.368853 + 0.929488i $$0.620249\pi$$
$$354$$ 0 0
$$355$$ 1.19394e6 + 2.06797e6i 0.502820 + 0.870910i
$$356$$ 0 0
$$357$$ 2.12919e6 + 3.68787e6i 0.884187 + 1.53146i
$$358$$ 0 0
$$359$$ −526967. + 912734.i −0.215798 + 0.373773i −0.953519 0.301332i $$-0.902569\pi$$
0.737721 + 0.675106i $$0.235902\pi$$
$$360$$ 0 0
$$361$$ −2.21470e6 + 1.10732e6i −0.894431 + 0.447205i
$$362$$ 0 0
$$363$$ 2.26525e6 3.92352e6i 0.902296 1.56282i
$$364$$ 0 0
$$365$$ 640529. + 1.10943e6i 0.251656 + 0.435881i
$$366$$ 0 0
$$367$$ −1.90021e6 3.29126e6i −0.736438 1.27555i −0.954089 0.299522i $$-0.903173\pi$$
0.217651 0.976027i $$-0.430160\pi$$
$$368$$ 0 0
$$369$$ 1.57200e6 0.601018
$$370$$ 0 0
$$371$$ −3.20791e6 5.55627e6i −1.21001 2.09579i
$$372$$ 0 0
$$373$$ −1.16264e6 −0.432685 −0.216342 0.976318i $$-0.569413\pi$$
−0.216342 + 0.976318i $$0.569413\pi$$
$$374$$ 0 0
$$375$$ −1.23141e6 + 2.13287e6i −0.452195 + 0.783225i
$$376$$ 0 0
$$377$$ −703663. + 1.21878e6i −0.254983 + 0.441643i
$$378$$ 0 0
$$379$$ −1.49509e6 −0.534648 −0.267324 0.963607i $$-0.586139\pi$$
−0.267324 + 0.963607i $$0.586139\pi$$
$$380$$ 0 0
$$381$$ 1.37330e6 0.484678
$$382$$ 0 0
$$383$$ −2.52086e6 + 4.36626e6i −0.878115 + 1.52094i −0.0247088 + 0.999695i $$0.507866\pi$$
−0.853407 + 0.521246i $$0.825467\pi$$
$$384$$ 0 0
$$385$$ 791634. 1.37115e6i 0.272190 0.471448i
$$386$$ 0 0
$$387$$ 3.08895e6 1.04842
$$388$$ 0 0
$$389$$ 612495. + 1.06087e6i 0.205224 + 0.355459i 0.950204 0.311628i $$-0.100874\pi$$
−0.744980 + 0.667087i $$0.767541\pi$$
$$390$$ 0 0
$$391$$ −1.38692e6 −0.458785
$$392$$ 0 0
$$393$$ 4.20350e6 + 7.28067e6i 1.37287 + 2.37788i
$$394$$ 0 0
$$395$$ −2.93980e6 5.09188e6i −0.948036 1.64205i
$$396$$ 0 0
$$397$$ −639677. + 1.10795e6i −0.203697 + 0.352813i −0.949717 0.313110i $$-0.898629\pi$$
0.746020 + 0.665924i $$0.231962\pi$$
$$398$$ 0 0
$$399$$ −1.12376e7 3.37522e6i −3.53378 1.06138i
$$400$$ 0 0
$$401$$ −473386. + 819928.i −0.147013 + 0.254633i −0.930122 0.367251i $$-0.880299\pi$$
0.783109 + 0.621884i $$0.213632\pi$$
$$402$$ 0 0
$$403$$ 1.13422e6 + 1.96453e6i 0.347885 + 0.602555i
$$404$$ 0 0
$$405$$ 6.59838e6 + 1.14287e7i 1.99894 + 3.46226i
$$406$$ 0 0
$$407$$ 269756. 0.0807208
$$408$$ 0 0
$$409$$ −1.78713e6 3.09540e6i −0.528260 0.914974i −0.999457 0.0329456i $$-0.989511\pi$$
0.471197 0.882028i $$-0.343822\pi$$
$$410$$ 0 0
$$411$$ 8.50856e6 2.48457
$$412$$ 0 0
$$413$$ −2.96644e6 + 5.13803e6i −0.855777 + 1.48225i
$$414$$ 0 0
$$415$$ 1.43538e6 2.48616e6i 0.409117 0.708611i
$$416$$ 0 0
$$417$$ −5.24984e6 −1.47845
$$418$$ 0 0
$$419$$ −4.64582e6 −1.29279 −0.646395 0.763003i $$-0.723724\pi$$
−0.646395 + 0.763003i $$0.723724\pi$$
$$420$$ 0 0
$$421$$ 1.59986e6 2.77104e6i 0.439923 0.761970i −0.557760 0.830002i $$-0.688339\pi$$
0.997683 + 0.0680329i $$0.0216723\pi$$
$$422$$ 0 0
$$423$$ 5.53877e6 9.59342e6i 1.50509 2.60689i
$$424$$ 0 0
$$425$$ −1.11697e6 −0.299963
$$426$$ 0 0
$$427$$ 2.49439e6 + 4.32041e6i 0.662056 + 1.14671i
$$428$$ 0 0
$$429$$ −1.60187e6 −0.420227
$$430$$ 0 0
$$431$$ 2.46054e6 + 4.26178e6i 0.638025 + 1.10509i 0.985866 + 0.167537i $$0.0535815\pi$$
−0.347841 + 0.937553i $$0.613085\pi$$
$$432$$ 0 0
$$433$$ 1.48931e6 + 2.57956e6i 0.381738 + 0.661189i 0.991311 0.131541i $$-0.0419924\pi$$
−0.609573 + 0.792730i $$0.708659\pi$$
$$434$$ 0 0
$$435$$ −2.40740e6 + 4.16973e6i −0.609992 + 1.05654i
$$436$$ 0 0
$$437$$ 2.78199e6 2.61999e6i 0.696871 0.656291i
$$438$$ 0 0
$$439$$ 1.08758e6 1.88374e6i 0.269339 0.466509i −0.699352 0.714777i $$-0.746528\pi$$
0.968691 + 0.248268i $$0.0798614\pi$$
$$440$$ 0 0
$$441$$ −1.47684e7 2.55795e7i −3.61606 6.26320i
$$442$$ 0 0
$$443$$ −189407. 328062.i −0.0458549 0.0794231i 0.842187 0.539186i $$-0.181268\pi$$
−0.888042 + 0.459763i $$0.847935\pi$$
$$444$$ 0 0
$$445$$ −3.94058e6 −0.943323
$$446$$ 0 0
$$447$$ −2.39760e6 4.15276e6i −0.567554 0.983032i
$$448$$ 0 0
$$449$$ −5.64067e6 −1.32043 −0.660214 0.751077i $$-0.729534\pi$$
−0.660214 + 0.751077i $$0.729534\pi$$
$$450$$ 0 0
$$451$$ −109766. + 190121.i −0.0254114 + 0.0440138i
$$452$$ 0 0
$$453$$ 6.64422e6 1.15081e7i 1.52124 2.63487i
$$454$$ 0 0
$$455$$ 1.10738e7 2.50766
$$456$$ 0 0
$$457$$ −317551. −0.0711252 −0.0355626 0.999367i $$-0.511322\pi$$
−0.0355626 + 0.999367i $$0.511322\pi$$
$$458$$ 0 0
$$459$$ 3.26888e6 5.66187e6i 0.724215 1.25438i
$$460$$ 0 0
$$461$$ 1.63141e6 2.82569e6i 0.357529 0.619259i −0.630018 0.776580i $$-0.716953\pi$$
0.987547 + 0.157322i $$0.0502859\pi$$
$$462$$ 0 0
$$463$$ −7.65368e6 −1.65927 −0.829636 0.558305i $$-0.811452\pi$$
−0.829636 + 0.558305i $$0.811452\pi$$
$$464$$ 0 0
$$465$$ 3.88044e6 + 6.72113e6i 0.832241 + 1.44148i
$$466$$ 0 0
$$467$$ 885237. 0.187831 0.0939155 0.995580i $$-0.470062\pi$$
0.0939155 + 0.995580i $$0.470062\pi$$
$$468$$ 0 0
$$469$$ −3.45528e6 5.98472e6i −0.725356 1.25635i
$$470$$ 0 0
$$471$$ −809439. 1.40199e6i −0.168125 0.291201i
$$472$$ 0 0
$$473$$ −215689. + 373583.i −0.0443276 + 0.0767777i
$$474$$ 0 0
$$475$$ 2.24050e6 2.11003e6i 0.455628 0.429096i
$$476$$ 0 0
$$477$$ −8.01448e6 + 1.38815e7i −1.61280 + 2.79345i
$$478$$ 0 0
$$479$$ 2.58332e6 + 4.47445e6i 0.514447 + 0.891047i 0.999859 + 0.0167625i $$0.00533592\pi$$
−0.485413 + 0.874285i $$0.661331\pi$$
$$480$$ 0 0
$$481$$ 943375. + 1.63397e6i 0.185918 + 0.322020i
$$482$$ 0 0
$$483$$ 1.81089e7 3.53203
$$484$$ 0 0
$$485$$ −951502. 1.64805e6i −0.183677 0.318138i
$$486$$ 0 0
$$487$$ −4.53740e6 −0.866931 −0.433465 0.901170i $$-0.642709\pi$$
−0.433465 + 0.901170i $$0.642709\pi$$
$$488$$ 0 0
$$489$$ −3.06988e6 + 5.31719e6i −0.580563 + 1.00556i
$$490$$ 0 0
$$491$$ −4.58323e6 + 7.93839e6i −0.857963 + 1.48603i 0.0159066 + 0.999873i $$0.494937\pi$$
−0.873869 + 0.486161i $$0.838397\pi$$
$$492$$ 0 0
$$493$$ 1.30530e6 0.241876
$$494$$ 0 0
$$495$$ −3.95556e6 −0.725596
$$496$$ 0 0
$$497$$ −4.22628e6 + 7.32014e6i −0.767481 + 1.32932i
$$498$$ 0 0
$$499$$ −4.86531e6 + 8.42697e6i −0.874700 + 1.51503i −0.0176190 + 0.999845i $$0.505609\pi$$
−0.857081 + 0.515181i $$0.827725\pi$$
$$500$$ 0 0
$$501$$ 8.07952e6 1.43811
$$502$$ 0 0
$$503$$ −5.37084e6 9.30257e6i −0.946503 1.63939i −0.752713 0.658349i $$-0.771255\pi$$
−0.193791 0.981043i $$-0.562078\pi$$
$$504$$ 0 0
$$505$$ −8.64888e6 −1.50915
$$506$$ 0 0
$$507$$ −115579. 200189.i −0.0199692 0.0345876i
$$508$$ 0 0
$$509$$ −2.77946e6 4.81416e6i −0.475516 0.823618i 0.524090 0.851663i $$-0.324405\pi$$
−0.999607 + 0.0280444i $$0.991072\pi$$
$$510$$ 0 0
$$511$$ −2.26733e6 + 3.92712e6i −0.384115 + 0.665307i
$$512$$ 0 0
$$513$$ 4.13870e6 + 1.75322e7i 0.694338 + 2.94132i
$$514$$ 0 0
$$515$$ −4.39294e6 + 7.60880e6i −0.729856 + 1.26415i
$$516$$ 0 0
$$517$$ 773497. + 1.33974e6i 0.127272 + 0.220441i
$$518$$ 0 0
$$519$$ −7.75785e6 1.34370e7i −1.26422 2.18970i
$$520$$ 0 0
$$521$$ −2.44377e6 −0.394427 −0.197213 0.980361i $$-0.563189\pi$$
−0.197213 + 0.980361i $$0.563189\pi$$
$$522$$ 0 0
$$523$$ 2.06842e6 + 3.58260e6i 0.330662 + 0.572723i 0.982642 0.185513i $$-0.0593948\pi$$
−0.651980 + 0.758236i $$0.726061\pi$$
$$524$$ 0 0
$$525$$ 1.45842e7 2.30931
$$526$$ 0 0
$$527$$ 1.05200e6 1.82211e6i 0.165002 0.285791i
$$528$$ 0 0
$$529$$ 269211. 466288.i 0.0418268 0.0724461i
$$530$$ 0 0
$$531$$ 1.48224e7 2.28130
$$532$$ 0 0
$$533$$ −1.53547e6 −0.234112
$$534$$ 0 0
$$535$$ 8.04093e6 1.39273e7i 1.21457 2.10369i
$$536$$ 0 0
$$537$$ 200825. 347839.i 0.0300526 0.0520526i
$$538$$ 0 0
$$539$$ 4.12485e6 0.611555
$$540$$ 0 0
$$541$$ 332076. + 575172.i 0.0487803 + 0.0844899i 0.889385 0.457160i $$-0.151133\pi$$
−0.840604 + 0.541650i $$0.817800\pi$$
$$542$$ 0 0
$$543$$ 2.18517e6 0.318043
$$544$$ 0 0
$$545$$ 1.82362e6 + 3.15860e6i 0.262992 + 0.455516i
$$546$$ 0 0
$$547$$ −2.27290e6 3.93678e6i −0.324797 0.562565i 0.656674 0.754174i $$-0.271963\pi$$
−0.981471 + 0.191609i $$0.938629\pi$$
$$548$$ 0 0
$$549$$ 6.23186e6 1.07939e7i 0.882443 1.52844i
$$550$$ 0 0
$$551$$ −2.61828e6 + 2.46581e6i −0.367398 + 0.346004i
$$552$$ 0 0
$$553$$ 1.04062e7 1.80241e7i 1.44704 2.50634i
$$554$$ 0 0
$$555$$ 3.22751e6 + 5.59021e6i 0.444769 + 0.770363i
$$556$$ 0 0
$$557$$ 4.10469e6 + 7.10954e6i 0.560586 + 0.970964i 0.997445 + 0.0714342i $$0.0227576\pi$$
−0.436859 + 0.899530i $$0.643909\pi$$
$$558$$ 0 0
$$559$$ −3.01717e6 −0.408386
$$560$$ 0 0
$$561$$ 742871. + 1.28669e6i 0.0996566 + 0.172610i
$$562$$ 0 0
$$563$$ −1.32458e7 −1.76119 −0.880597 0.473866i $$-0.842858\pi$$
−0.880597 + 0.473866i $$0.842858\pi$$
$$564$$ 0 0
$$565$$ −4.05835e6 + 7.02927e6i −0.534846 + 0.926380i
$$566$$ 0 0
$$567$$ −2.33567e7 + 4.04550e7i −3.05109 + 5.28464i
$$568$$ 0 0
$$569$$ 1.11112e7 1.43873 0.719365 0.694632i $$-0.244433\pi$$
0.719365 + 0.694632i $$0.244433\pi$$
$$570$$ 0 0
$$571$$ 1.44176e7 1.85055 0.925277 0.379291i $$-0.123832\pi$$
0.925277 + 0.379291i $$0.123832\pi$$
$$572$$ 0 0
$$573$$ 7.72172e6 1.33744e7i 0.982489 1.70172i
$$574$$ 0 0
$$575$$ −2.37497e6 + 4.11356e6i −0.299563 + 0.518858i
$$576$$ 0 0
$$577$$ −4.63470e6 −0.579538 −0.289769 0.957097i $$-0.593578\pi$$
−0.289769 + 0.957097i $$0.593578\pi$$
$$578$$ 0 0
$$579$$ 366782. + 635285.i 0.0454686 + 0.0787539i
$$580$$ 0 0
$$581$$ 1.01618e7 1.24891
$$582$$ 0 0
$$583$$ −1.11923e6 1.93857e6i −0.136380 0.236217i
$$584$$ 0 0
$$585$$ −1.38331e7 2.39597e7i −1.67121 2.89462i
$$586$$ 0 0
$$587$$ −87378.3 + 151344.i −0.0104667 + 0.0181288i −0.871211 0.490908i $$-0.836665\pi$$
0.860745 + 0.509037i $$0.169998\pi$$
$$588$$ 0 0
$$589$$ 1.33193e6 + 5.64224e6i 0.158195 + 0.670137i
$$590$$ 0 0
$$591$$ 5.36854e6 9.29858e6i 0.632248 1.09509i
$$592$$ 0 0
$$593$$ 63610.1 + 110176.i 0.00742830 + 0.0128662i 0.869716 0.493553i $$-0.164302\pi$$
−0.862287 + 0.506419i $$0.830969\pi$$
$$594$$ 0 0
$$595$$ −5.13551e6 8.89497e6i −0.594691 1.03003i
$$596$$ 0 0
$$597$$ −2.40403e6 −0.276061
$$598$$ 0 0
$$599$$ 8.00216e6 + 1.38601e7i 0.911255 + 1.57834i 0.812293 + 0.583249i $$0.198219\pi$$
0.0989618 + 0.995091i $$0.468448\pi$$
$$600$$ 0 0
$$601$$ 1.52423e7 1.72134 0.860668 0.509166i $$-0.170046\pi$$
0.860668 + 0.509166i $$0.170046\pi$$
$$602$$ 0 0
$$603$$ −8.63250e6 + 1.49519e7i −0.966815 + 1.67457i
$$604$$ 0 0
$$605$$ −5.46367e6 + 9.46336e6i −0.606871 + 1.05113i
$$606$$ 0 0
$$607$$ 1.49576e7 1.64774 0.823870 0.566778i $$-0.191810\pi$$
0.823870 + 0.566778i $$0.191810\pi$$
$$608$$ 0 0
$$609$$ −1.70432e7 −1.86213
$$610$$ 0 0
$$611$$ −5.41005e6 + 9.37049e6i −0.586271 + 1.01545i
$$612$$ 0 0
$$613$$ 889245. 1.54022e6i 0.0955807 0.165551i −0.814270 0.580486i $$-0.802863\pi$$
0.909851 + 0.414936i $$0.136196\pi$$
$$614$$ 0 0
$$615$$ −5.25322e6 −0.560064
$$616$$ 0 0
$$617$$ 7.97293e6 + 1.38095e7i 0.843150 + 1.46038i 0.887218 + 0.461350i $$0.152635\pi$$
−0.0440683 + 0.999029i $$0.514032\pi$$
$$618$$ 0 0
$$619$$ −1.53524e7 −1.61046 −0.805231 0.592962i $$-0.797959\pi$$
−0.805231 + 0.592962i $$0.797959\pi$$
$$620$$ 0 0
$$621$$ −1.39010e7 2.40773e7i −1.44650 2.50541i
$$622$$ 0 0
$$623$$ −6.97438e6 1.20800e7i −0.719922 1.24694i
$$624$$ 0 0
$$625$$ 6.02615e6 1.04376e7i 0.617078 1.06881i
$$626$$ 0 0
$$627$$ −3.92076e6 1.17761e6i −0.398292 0.119628i
$$628$$ 0 0
$$629$$ 874985. 1.51552e6i 0.0881807 0.152734i
$$630$$ 0 0
$$631$$ 1.84277e6 + 3.19177e6i 0.184246 + 0.319123i 0.943322 0.331879i $$-0.107682\pi$$
−0.759076 + 0.651002i $$0.774349\pi$$
$$632$$ 0 0
$$633$$ −6.96173e6 1.20581e7i −0.690570 1.19610i
$$634$$ 0 0
$$635$$ −3.31234e6 −0.325988
$$636$$ 0 0
$$637$$ 1.44252e7 + 2.49851e7i 1.40855 + 2.43968i
$$638$$ 0 0
$$639$$ 2.11175e7 2.04592
$$640$$ 0 0
$$641$$ 2.60486e6 4.51176e6i 0.250403 0.433711i −0.713234 0.700926i $$-0.752770\pi$$
0.963637 + 0.267215i $$0.0861035\pi$$
$$642$$ 0 0
$$643$$ 3.62947e6 6.28642e6i 0.346191 0.599620i −0.639379 0.768892i $$-0.720808\pi$$
0.985569 + 0.169272i $$0.0541417\pi$$
$$644$$ 0 0
$$645$$ −1.03225e7 −0.976976
$$646$$ 0 0
$$647$$ −8.49406e6 −0.797728 −0.398864 0.917010i $$-0.630595\pi$$
−0.398864 + 0.917010i $$0.630595\pi$$
$$648$$ 0 0
$$649$$ −1.03499e6 + 1.79265e6i −0.0964545 + 0.167064i
$$650$$ 0 0
$$651$$ −1.37359e7 + 2.37912e7i −1.27029 + 2.20021i
$$652$$ 0 0
$$653$$ −1.16393e7 −1.06818 −0.534089 0.845428i $$-0.679345\pi$$
−0.534089 + 0.845428i $$0.679345\pi$$
$$654$$ 0 0
$$655$$ −1.01386e7 1.75606e7i −0.923372 1.59933i
$$656$$ 0 0
$$657$$ 1.13291e7 1.02396
$$658$$ 0 0
$$659$$ −9.86735e6 1.70907e7i −0.885089 1.53302i −0.845612 0.533798i $$-0.820764\pi$$
−0.0394769 0.999220i $$-0.512569\pi$$
$$660$$ 0 0
$$661$$ 7.97821e6 + 1.38187e7i 0.710235 + 1.23016i 0.964769 + 0.263099i $$0.0847446\pi$$
−0.254534 + 0.967064i $$0.581922\pi$$
$$662$$ 0 0
$$663$$ −5.19585e6 + 8.99947e6i −0.459063 + 0.795121i
$$664$$ 0 0
$$665$$ 2.71045e7 + 8.14088e6i 2.37677 + 0.713867i
$$666$$ 0 0
$$667$$ 2.77542e6 4.80717e6i 0.241554 0.418384i
$$668$$ 0 0
$$669$$ −1.92128e7 3.32775e7i −1.65968 2.87465i
$$670$$ 0 0
$$671$$ 870288. + 1.50738e6i 0.0746202 + 0.129246i
$$672$$ 0 0
$$673$$ 1.18685e7 1.01008 0.505041 0.863096i $$-0.331477\pi$$
0.505041 + 0.863096i $$0.331477\pi$$
$$674$$ 0 0
$$675$$ −1.11953e7 1.93908e7i −0.945750 1.63809i
$$676$$ 0 0
$$677$$ −1.13643e7 −0.952952 −0.476476 0.879188i $$-0.658086\pi$$
−0.476476 + 0.879188i $$0.658086\pi$$
$$678$$ 0 0
$$679$$ 3.36810e6 5.83372e6i 0.280356 0.485591i
$$680$$ 0 0
$$681$$ 1.08374e6 1.87709e6i 0.0895482 0.155102i
$$682$$ 0 0
$$683$$ 1.33134e7 1.09204 0.546018 0.837774i $$-0.316143\pi$$
0.546018 + 0.837774i $$0.316143\pi$$
$$684$$ 0 0
$$685$$ −2.05223e7 −1.67109
$$686$$ 0 0
$$687$$ 1.85051e7 3.20517e7i 1.49589 2.59095i
$$688$$ 0 0
$$689$$ 7.82824e6 1.35589e7i 0.628226 1.08812i
$$690$$ 0 0
$$691$$ 1.77578e7 1.41480 0.707400 0.706813i $$-0.249868\pi$$
0.707400 + 0.706813i $$0.249868\pi$$
$$692$$ 0 0
$$693$$ −7.00088e6 1.21259e7i −0.553757 0.959136i
$$694$$ 0 0
$$695$$ 1.26624e7 0.994381
$$696$$ 0 0
$$697$$ 712079. + 1.23336e6i 0.0555196 + 0.0961628i
$$698$$ 0 0
$$699$$ 1.60958e7 + 2.78787e7i 1.24600 + 2.15814i
$$700$$ 0 0
$$701$$ 2.58452e6 4.47652e6i 0.198648 0.344069i −0.749442 0.662070i $$-0.769678\pi$$
0.948090 + 0.318001i $$0.103012\pi$$
$$702$$ 0 0
$$703$$ 1.10781e6 + 4.69286e6i 0.0845429 + 0.358137i
$$704$$ 0 0
$$705$$ −1.85091e7 + 3.20586e7i −1.40253 + 2.42925i
$$706$$ 0 0
$$707$$ −1.53075e7 2.65134e7i −1.15175 1.99488i
$$708$$ 0 0
$$709$$ 6.35081e6 + 1.09999e7i 0.474476 + 0.821816i 0.999573 0.0292265i $$-0.00930441\pi$$
−0.525097 + 0.851042i $$0.675971\pi$$
$$710$$ 0 0
$$711$$ −5.19967e7 −3.85746
$$712$$ 0 0
$$713$$ −4.47366e6 7.74860e6i −0.329563 0.570820i
$$714$$ 0 0
$$715$$ 3.86364e6 0.282638
$$716$$ 0 0
$$717$$ −1.37178e7 + 2.37600e7i −0.996524 + 1.72603i
$$718$$ 0 0
$$719$$ 1.17643e7 2.03763e7i 0.848678 1.46995i −0.0337101 0.999432i $$-0.510732\pi$$
0.882388 0.470522i $$-0.155934\pi$$
$$720$$ 0 0
$$721$$ −3.11000e7 −2.22804
$$722$$ 0 0
$$723$$ 2.94021e6 0.209186
$$724$$ 0 0
$$725$$ 2.23520e6 3.87149e6i 0.157933 0.273548i
$$726$$ 0 0
$$727$$ 1.08765e7 1.88387e7i 0.763229 1.32195i −0.177949 0.984040i $$-0.556946\pi$$
0.941178 0.337911i $$-0.109720\pi$$
$$728$$ 0 0
$$729$$ 3.44949e7 2.40401
$$730$$ 0 0
$$731$$ 1.39922e6 + 2.42352e6i 0.0968485 + 0.167746i
$$732$$ 0 0
$$733$$ −9.80139e6 −0.673795 −0.336897 0.941541i $$-0.609378\pi$$
−0.336897 + 0.941541i $$0.609378\pi$$
$$734$$ 0 0
$$735$$ 4.93519e7 + 8.54800e7i 3.36965 + 5.83641i
$$736$$ 0 0
$$737$$ −1.20554e6 2.08806e6i −0.0817548 0.141603i
$$738$$ 0 0
$$739$$ −7.08883e6 + 1.22782e7i −0.477489 + 0.827035i −0.999667 0.0258011i $$-0.991786\pi$$
0.522178 + 0.852837i $$0.325120\pi$$
$$740$$ 0 0
$$741$$ −6.57842e6 2.78672e7i −0.440125 1.86444i
$$742$$ 0 0
$$743$$ −3.04168e6 + 5.26834e6i −0.202135 + 0.350108i −0.949216 0.314625i $$-0.898121\pi$$
0.747081 + 0.664733i $$0.231455\pi$$
$$744$$ 0 0
$$745$$ 5.78289e6 + 1.00163e7i 0.381728 + 0.661173i
$$746$$ 0 0
$$747$$ −1.26939e7 2.19865e7i −0.832327 1.44163i
$$748$$ 0 0
$$749$$ 5.69261e7 3.70772
$$750$$ 0 0
$$751$$ 6.05235e6 + 1.04830e7i 0.391584 + 0.678243i 0.992659 0.120950i $$-0.0385941\pi$$
−0.601075 + 0.799193i $$0.705261\pi$$
$$752$$ 0 0
$$753$$ 1.12318e7 0.721878
$$754$$ 0 0
$$755$$ −1.60255e7 + 2.77571e7i −1.02316 + 1.77217i
$$756$$ 0 0
$$757$$ −837126. + 1.44994e6i −0.0530947 + 0.0919627i −0.891351 0.453313i $$-0.850242\pi$$
0.838257 + 0.545276i $$0.183575\pi$$
$$758$$ 0 0
$$759$$ 6.31817e6 0.398095
$$760$$ 0 0
$$761$$ −1.71108e7 −1.07105 −0.535525 0.844520i $$-0.679886\pi$$
−0.535525 + 0.844520i $$0.679886\pi$$
$$762$$ 0 0
$$763$$ −6.45519e6 + 1.11807e7i −0.401419 + 0.695278i
$$764$$ 0 0
$$765$$ −1.28303e7 + 2.22227e7i −0.792653 + 1.37292i
$$766$$ 0 0
$$767$$ −1.44780e7 −0.888626
$$768$$ 0 0
$$769$$ −4.88795e6 8.46617e6i −0.298065 0.516263i 0.677628 0.735404i $$-0.263008\pi$$
−0.975693 + 0.219141i $$0.929674\pi$$
$$770$$ 0 0
$$771$$ 3.26645e7 1.97897
$$772$$ 0 0
$$773$$ −6.30084e6 1.09134e7i −0.379271 0.656916i 0.611686 0.791101i $$-0.290492\pi$$
−0.990956 + 0.134185i $$0.957158\pi$$
$$774$$ 0 0
$$775$$ −3.60289e6 6.24039e6i −0.215475 0.373214i
$$776$$ 0 0
$$777$$ −1.14246e7 + 1.97880e7i −0.678875 + 1.17585i
$$778$$ 0 0
$$779$$ −3.75825e6 1.12880e6i −0.221892 0.0666457i
$$780$$ 0 0
$$781$$ −1.47454e6 + 2.55398e6i −0.0865027 + 0.149827i
$$782$$ 0 0
$$783$$ 1.30830e7 + 2.26604e7i 0.762610 + 1.32088i
$$784$$ 0 0
$$785$$ 1.95233e6 + 3.38154e6i 0.113078 + 0.195857i
$$786$$ 0 0
$$787$$ −1.91406e7 −1.10159 −0.550795 0.834641i $$-0.685675\pi$$
−0.550795 + 0.834641i $$0.685675\pi$$
$$788$$ 0 0
$$789$$ −8.15667e6 1.41278e7i